A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. She wants the area to be 225 square yards. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

I don't just want an answer I want to know how to do this.

Question

A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter base to be 3 yards greater than the height, and the longer base to be 7 yards greater than the height. She wants the area to be 225 square yards. Use the Quadratic Formula to find the height that will give the desired area. Round to the nearest hundredth of a yard.

I don't just want an answer I want to know how to do this.

mathstudent55 · Answer

Area of trapezoid = (1/2)(a + b)h, where a and b are the lengths of the bases, and h is the height.
height = h
shorter base = h + 3
longer base = h + 7
A = 225
A = (1/2)(a + b)h using above numbers for a, b, and A:
225 = (1/2)(h + 3 + h + 7)h
450 = (2h + 10)h
450 = 2h^2 + 10h
2h^2 + 10h - 450 = 0
Divide both sides by 2:
h^2 + 5h - 225 = 0
Now use the quadratic formula to get h.

anonymous · Answer

okay... somehow I got to (h=5)^2=450 and I don't know what to do next or if I'm even on the right track.

anonymous · Answer

ooops, that is supposed to say (h+5)^2=450

mathstudent55 · Answer

Your eq is not correct.
Continue with h^2 + 5h - 225 = 0
Use the quadratic formula with this equation.

anonymous · Answer

so (h+5)^2=225?

anonymous · Answer

h+5=15?

mathstudent55 · Answer

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